Comparison of nonlinear model-based controllers and gain-scheduled Internal Model Control based on identified model Esmaeil Jahanshahi and Sigurd Skogestad Department of Chemical Engineering NTNU Trondheim, Norway Two-phase pipe flow (liquid and vapor) Slug (liquid) buildup CDC, December 2013 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAA

Slug cycle (stable limit cycle) Experiments performed by the Multiphase Laboratory, NTNU

Experimental mini-loop (2003) Ingvald Bårdsen, Espen Storkaas, Heidi Sivertsen

Experimental mini-loop Valve opening (z) = 100% SLUGGING

Experimental mini-loop Valve opening (z) = 25% SLUGGING

Experimental mini-loop Valve opening (z) = 15% NO SLUG

Experimental mini-loop: Bifurcation diagram z Experimental mini-loop: Bifurcation diagram No slug Valve opening z % Slugging

How to avoid slugging?

Avoid slugging: 1. Close valve (but increases pressure) z Design change Avoid slugging: 1. Close valve (but increases pressure) No slugging when valve is closed Valve opening z %

Avoid slugging: 2. Design change to avoid slugging p1 p2 z

Minimize effect of slugging: 3. Build large slug-catcher Design change Minimize effect of slugging: 3. Build large slug-catcher Most common strategy in practice p1 p2 z

Avoid slugging: 4. ”Active” feedback control PT PC ref Simple PI-controller p1 z

Anti slug control: Mini-loop experiments p1 [bar] z [%] Controller ON Controller OFF

Anti slug control: Full-scale offshore experiments at Hod-Vallhall field (Havre,1999)

Fundamental limitation – top pressure Measuring topside pressure we can stabilize the system only in a limited range Unstable (RHP) zero dynamics of top pressure Z = 20% Z = 40% Ms,min 2.1 7.0

Summary anti slug control (2008)* Stabilization of desired non-slug flow regime = $$$$! Stabilization using downhole pressure simple Stabilization using topside measurements difficult Control can make a difference! “Only” problem: Not sufficiently robust *Thanks to: Espen Storkaas + Heidi Sivertsen + Håkon Dahl-Olsen + Ingvald Bårdsen

New Experimental mini-rig 2009-2013: Esmaeil Jahanshahi, PhD-work supported by Siemens New Experimental mini-rig 3m

1st step: Developed new simple 4-state model*. θ h L2 hc wmix,out x1, P1,VG1, ρG1, HL1 x3, P2,VG2, ρG2 , HLT P0 Choke valve with opening Z x4 h>hc wG,lp=0 wL,lp L3 wL,in wG,in w x2 L1 State equations (mass conservations law): *Based on Storkaas model

New 4-state model. Comparison with experiments: Top pressure Subsea pressure Nonlinear: Process gain = slope - approaches zero for large z

Linear Control Solutions

Experiment Linear Solution 1: H∞ control by linearizing new model Experiment, mixed-sensitivity design

Experimental linear model (new approach) Fourth-order mechanistic model: Closed-loop step-response with P-control Hankel Singular Values: Model reduction: 4 parameters need to be estimated

Linear Solution 2: IMC based on identified model IMC design Block diagram for Internal Model Control system IMC for unstable systems: Model: y u e r + _ Plant IMC controller:

Linear Solution 2: IMC based on identified model Experiment

Linear Solution 3: «Robustified» IMC using H∞ loop shaping Experiment Linear Solution 3: «Robustified» IMC using H∞ loop shaping

Comparing linear controllers (subsea pressure) * *Controllers tuned at 30% valve opening

Nonlinear Control Solutions

Solution 1: observer & state feedback PT Nonlinear observer K State variables uc Pt

High-Gain Observer

State Feedback Kc : linear optimal gain calculated by solving Riccati equation Ki : small integral gain (e.g. Ki = 10−3)

High-gain observer – top pressure Experiment High-gain observer – top pressure measurement: topside pressure valve opening: 20 %

High-gain observer – subsea pressure Open-loop experiment High-gain observer – subsea pressure measurement: subsea pressure valve opening: 20 % Closed-loop: Not working !!?

Chain of Integrators Fast nonlinear observer using subsea pressure: Not Working??! Pipeline-riser system is a chain of integrator Measuring top pressure and estimating subsea pressure is differentiating Measuring subsea pressure and estimating top pressure is integrating x

Solution 2: feedback linearization PT Nonlinear controller uc Prt Jahanshahi, Skogestad and Grøtli, NOLCOS, 2013

Output-linearizing controller Stabilizing controller for riser subsystem System in normal form: : riser-base pressure : top pressure Linearizing controller: dynamics bounded Control signal to valve:

CV: riser-base pressure (y1), Z=60% Experiment CV: riser-base pressure (y1), Z=60% Gain:

Solution 3: Gain-Scheduled IMC Three identified model from step tests: Z=20%: Z=30%: Z=40%: Three IMC controllers:

Solution 3: Gain-Scheduled IMC Experiment

Comparison of Nonlinear Controllers Gain-scheduling IMC is the most robust solution Adaptive PI controller is the second-best Controllability remarks: Fundamental limitation control: gain of the system goes to zero for fully open valve Additional limitation top-side pressure: Inverse response (non-minimum-phase)

Conclusions System is strongly nonlinear Must increase controller gain for large valve openings (lower pressure) Rank of nonlinear controllers for anti-slug control (using subsea pressure): Gain-scheduled IMC Feedback linearization High-gain observer (doesn’t work) More recently, even better: Robustified gain-scheduled IMC using H-infinity loop shaping Loop transfer recovery based on LQG-controller Acknowledgements Financial support from SIEMENS Master students: Elisabeth Hyllestad, Anette Helgesen, Knut Åge Meland, Mats Lieungh, Henrik Hansen, Terese Syre, Mahnaz Esmaeilpour and Anne Sofie Nilsen.